Not sure what the Amiibos themselves will do, we still don't have much details, but those and the cards will be compatible and on top of that there will be a new series of cards with new villagers on them. The update will also get rid of any weeds currently in your town as a nice gesture. I believe at least the New Villagers can move into your town if you don't have a full town but other than that the details are very little.
EDIT: It also appears Non Animal Crossing Amiibo can provide new themed Furniture from their Series.
http://www.nintendo.com/amiibo/games/detail/animal-crossing-new-leaf-3dsEDIT 2: In addition there's going to be a "new" edition of New Leaf called New Leaf Welcome Amiibo available with the update already applied and all New Leaf Copies sold from then will be that edition. Very handy for any one that doesn't have internet access for one reason or another.
EDIT 3: Okay I got some things mixed up, the current Villager Cards can be used to have those Villagers move in, the New ones live in Mobile Homes and can also move in. An Animal Crossing Mini Direct is coming in the Fall to go more in depth about the Amiibo functionality.